To solve this question, let's first understand what an average is. The average of a set of numbers is the total sum of those numbers divided by the number of items in that set.
Given that, if the average of a few numbers is 25, it means that if we added all of the numbers together and divided by the count of those numbers, our result would be 25.
Now, if we increase every number in our set by 5, what happens to the average?
Let's go through this step-by-step:
1. Let's say there are 'n' natural numbers in the set. We don't know what these numbers are, but we know their average is 25.
2. This means that the total sum of all the natural numbers is 25 n, since average = (sum of all terms) / (number of terms).
3. Now, if we increase each natural number by 5, we are increasing the total sum of the numbers by 5 n, because each of the 'n' numbers has 5 added to it.
4. The new total sum of all numbers would, therefore, be (25 n) + (5 n).
5. This simplifies to 25n + 5n, which can be combined into 30n.
6. Now, the new average is the new total sum divided by the number of terms, which has not changed. It is still 'n'.
7. The new average would be (30n) / n, which simplifies to just 30.
Therefore, the new average, after increasing every number by 5, is 30. This method shows that when the same amount is added to every term in a set of numbers, the average of the set increases by that same amount.
